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The International Monetary Fund’s new chief foresees “real nasty consequences” for the U.S. and global economies if the U.S. fails to raise its borrowing limit.

Christine Lagarde, the first woman to head the lending institution, said in an interview broadcast Sunday that such a failure would cause interest rates to rise and stock markets to fall.

That would threaten an important IMF goal, which is preserving stability in the world economy, she said.

The U.S. borrowing limit is $14.3 trillion. Obama administration officials say the U.S. would begin to default without an agreement by Aug. 2.

“If you draw out the entire scenario of default, yes, of course, you have all of that - interest hikes, stock markets taking a huge hit and real nasty consequences, not just for the United States, but for the entire global economy, because the U.S. is such a big player and matters so much for other countries,” she said.

Ms. Lagarde, who took over as managing director Tuesday, also addressed the fallout stemming from the sexual assault charges filed against her predecessor, Dominique Strauss-Kahn.

Mr. Strauss-Kahn resigned in May after he was accused of attacking a hotel maid in New York City. He has denied the charge. New York prosecutors have admitted in recent weeks that their case has weakened and that the accuser has lied about many aspects of her background.

“When it comes to ethics and whatever I do, I always think to myself, would my mother approve of that,” she said. “And if she did not, then there’s something wrong.”

Ms. Lagarde did not address the European debt crisis or the IMF’s recent aid to Greece. On Friday, the IMF’s board approved a $4.2 billion loan to Greece, the latest installment of a bailout package intended to prevent the struggling nation from defaulting on its debt.

The IMF, with 187 member nations, lends money to countries with troubled finances.